﻿898 



Mr. T. H. Blakesley: A Kinematic 



the sketch, not both within the right angle, complete the 

 small rhombus of one of them by adding the short bars bb. 



Also take AB equal to b, and AD equal to a, the two sides 

 of the last cosine kite. Between D and B insert the bars 

 DE, EB, equal respectively to a and b. Complete the 

 rhombus BACF with bars, and join FH, FE with bars each 

 equal to y/2 . b. 



Then AE will be always equal to AH, and at right angles 

 to it. 



The chord r n of the sine linkage always bears the same 

 relation to AE, and therefore also to AH which is B. n . 



The proof of this construction is seen at once by noting 

 that the outlining bars of the figure A-B-E-F-H-C-A, with 

 the additional links FB,FC, constitute a Sylvester pantograph 

 of the form in which the ratio of the radii is one of equality, 

 and the angle between them 90°. 



In the case of n being even, sufficient expression has been 

 given to the method to be observed; but when n is odd the 

 first chord R : makes an angle of 6 only with 0.i% whereas 

 the common angle between the chords externally is 20. 



To secure that R x shall be maintained at the proper angle, 

 add to the system a kite equal in all respects to the first and 

 preceding it (fig. 5). Connect by two equal bars d d either 



Fig. 5. 



the heads or tails of the two kites, and joining these bars by a 

 joint at their other extremities, maintain the point of junction 

 in the line of reference Oy. The motion will then be as 

 desired. 



It is not necessary that a problem should be stated as an 



